Why don't nerve and muscle cells undergo mitosis?

Go to the link and scroll way down to G2 Phase for a short answer:

http://www.dartmouth.edu/~cbbc/courses/bio4/bio4-1997/02-theCell.html

Nerve and muscle cells do not undergo mitosis because they have exited the cell cycle and entered a state called G0 phase. This means that they are in a non-dividing phase and have reached a specialized and differentiated state.

To understand this in more detail, you can follow the link provided. Once you open the link, scroll down to G2 Phase. Here you can find a brief explanation of the cell cycle and the different phases involved, including G0 phase. This will help you understand why nerve and muscle cells do not undergo mitosis.